Maths Dictionary http://mrcrammond.com/games/2ring-centrev4.swf Week 8 Term 3 Mr Potter has set the task of ‘walking the length’ of State Highway 1 in 50 school days. You are allowed to count each step that each student takes if you walk to and from school and if you walk laps of the 400 m track on the school field at fitness time.
Use the data the class have collected below, to work out how many laps of the track each student will need to walk on each of the 50 challenge days.
How do we get to school?
Walk
6
Ride
2
Scoot/skate
4
Bus
5
Car
11
How many metres do each of the walkers take? (Each walker used a gps app on a smartphone to measure their walk to school)
250, 186, 373, 1256, 812, 280 Week 3 Term 3
Venue of the 2016 Summer Olympic Games Population of Rio: 6.4 million
Area of Rio: 1256 square kilometres (km2)
Founded: 1565
No. of days of competition: 17
No. of athletes competing: 10, 500
Medal events: 306
No. of security forces: 85, 000
The Steepest Street in the World
Dunedin, in New Zealand, claims to have the world's steepest paved road. However some people challenge Baldwin Street's slope and say mapping error has given it a gradient of 1 in 2.66, or 38%. However, it is almost impossible to ride a bike up or down it. Many of the stiffest road climbs for cyclists are on the Austrian side of the Dolomites (Halltall rises to 1482m in 7km at an average of 14%, its steepest stretch being 32%).
In France from the top of the legendary 1909m Mont Ventoux, there's around 1500m of descent in 21km averaging 7.5%; Iseran's 2770m peak offers 37km of descent and Alpe d'Huez has 21 hairpins.
San Francisco in the USA has some seriousoly steep streets. Take Lombard Street, a short streetcar ride from Fisherman's Wharf. This tourist photostop appeared for years in the Guinness Book of Records under its 'steepest street' entry, despite not even being the steepest street in San Francisco. At 1 in 5.5, or 18%, it's a mere slope compared to neighbouring Filbert St, San Francisco's actual steepest at 1 in 3.2, or 31.5% (22nd St is also 31.5%).
So it looks like Baldwin Street (pictured) may be the steepest after all.
Sample instructions to read to students
Draw a small triangle in the middle of your page.
Draw a circle in the triangle.
Above the triangle, draw a square.
At the bottom of the page on the left, draw an oval.
At the bottom of the page on the right, draw a rectangle.
Between the oval and the rectangle, draw a square.
Write the numbers 1–9 across the top of your page.
Draw three circles under the triangle.
On the right of the page at the top, draw a big triangle.
In the big triangle, draw a square.
Sample picture
Write a summary about being introduced to Sumdog
What experience do you have in using computers for learning? What is liked about Sumdog? Do you enjoy learning maths? Has your attitude changed? Do you use Sumdog outside the classroom? If so are there any issues? What could be improved? http://www.teachinabox.com.au/iteminfo.aspx?itemid=3058#productInfo
Problem Challenge is a mathematics problem solving competition aimed primarily at children in years 7 and 8 but may be of interest to mathematically gifted children in year 6. It has been offered to schools throughout New Zealand for the past 25 years.
544 and 760 are both three-digit numbers whose digits add to 13.
What is the smallest three-digit number whose digits add to 13?
Bob managed to colour the different regions in this map using just three colours: red, green and blue. He did it so that no two adjacent regions had the same colour.
If he coloured region 1 blue and region 2 red, what colour did he use for region X?
Supa Cycles make both two-wheeled bicycles and three-wheeled tricycles. Last week they made 12 in total, and used 31 wheels. How many tricycles did they make?
Enter one A, one B and one C in each row and column of this design of 16 squares, leaving four squares empty. When viewed along one of the arrows the first letter you must see is the letter given.
Give the last row from left to right, using * for the empty square (e.g. A*BC).
One-tenth of the cars in a car park are yellow. Another car arrives and now one-ninth of the cars are yellow. How many cars are now in the car park?
Image
2015
SET FOUR
Image
Time allowed - 30 minutes
Jeremy pays the exact amount for his new $17 T-shirt using $5 notes and $2 coins only.
In how many different ways can he do this?
There are three children in the Fong family and only one is a teenager. When their ages are multiplied together the result is 140.
How old is the teenager?
The three symbols in this design stand for numbers, where each row and each column has the total given.
What is the value of ♥ ?
The pages of a book are numbered 1, 2, 3, ... . In total, it takes 489 digits to number all the pages of the book.
What is the number on the last numbered page?
NZ National Maths Contest - 10 Jun to 16 Jun
This contest has now finished. Congratulations to all those who took part!
Leo the Rabbit is climbing up a flight of 10 steps. Leo can only hop up 1 or 2 steps each time he hops. He never hops down, only up. How many different ways can Leo hop up the flight of 10 steps? Provide evidence to justify your thinking.
=
=
If there is only one stair, then there is only one way to climb this stair.
If there are two stairs, then there are two ways to climb the stairs, by taking two steps or one big step (covering two stairs) If there are three stairs, then the rabbit can take 3 small steps take a big step and then a small one or a small step followed by a big step. If there are four stairs, then the rabbit can climb the stairs in
four small steps
two small steps and a large step
one small step, then a large, then a small
one large step, then two small steps
or two large steps Thus we have
Number of steps
1
2
3
4
Number of ways to climb the steps
1
2
3
5
Now look at the four step problem with a "looking backwards" strategy. Suppose the rabbit has just arrived at the top. It got there either by being on the third step and hopping up one step or it was on the second step and got there by hopping up two steps. From what we did before there are 3 ways to get to step three and 2 ways to get to step two. Thus, there are 3 + 2 = 5 ways to get to step four. Similarly for a 5 step flight of stairs there are 5 ways to get to step four and 3 ways to get to step three and thus there are 5 + 3 = 8 ways to get to step five. So now we have
Number of steps
1
2
3
4
5
Number of ways to climb the steps
1
2
3
5
8
The pattern in the bottom row of the table should now be clear. Each number in this row (after the first two) is the sum of the two previous numbers. Thus it is easy to continue this row. 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10,944,... Hence there are 89 nine ways for the rabbit to climb ten stairs (and 10,944 ways for it to climb 20 stairs!)
Level 4 number
Anno’s mysterious multiplying jar, by Masaichiro and Mitsumasa Anno
Follow 12 year-old Robert as he does battle with his attitude to maths each night in his dreams as he is visited by The Number Devil. An illustrated novel that presents complex (and simple) mathematical concepts in engaging ways.
An illustrated series of short non-fiction articles on topics involving very large and very small numbers. It all depends on what you’re measuring.
Mathematics
Measurement, large numbers, decimals, million, time size, distance.
A story of natural numbers, by David Demant
Publisher: Black Dog Books ISBN: 9781742030289
Description
A graphically engaging and colourful illustrated non-fiction book about 0-1-2-3-4-5-6-7-8-9, their history, uses and power.
Mathematics
Natural numbers, calculation, bases, number systems.
Murderous maths numbers: the key to the universe, by Kjartan Poskitt
Publisher: Scholastic ISBN: 0439981166
Description
One of the Murderous Maths large series of humourous non-fiction books that explore the world of mathematics with cartoons, engaging and quirky contexts and diagrams. Filled with puzzles and problems and “no boring sums!”.
Mathematics
Number, algebra, bases, sequences, calculation.
50 Amazing Things Kids Need to Know about Mathematics, by Anne Rooney
Publisher: Quercus Books UK (2011) ISBN: 9780857386021
Sumdog's Canterbury Maths Contest is now underway.
As it progresses, you'll find the latest scores on the leaderboards: Contest leaderboards
Monday 14th March Here are the results from the classes in your school:
Class
Students played
Score
Position
M12016
16
164
3rd
For a class to qualify for the leaderboards, at least 10 students from that class must play in the contest.
Friday 11th March
Top 10 classes
Overall class scores are the average number of correct answers out of the students in that class. At least 10 students from the class must have played in order to get an average score.
Term 4Ratios
Percentages
NEXT STEP CONVERT TO A DECIMAL
Week 9 Term 3
Maths Dictionary
http://mrcrammond.com/games/2ring-centrev4.swf
Week 8 Term 3
Mr Potter has set the task of ‘walking the length’ of State Highway 1 in 50 school days. You are allowed to count each step that each student takes if you walk to and from school and if you walk laps of the 400 m track on the school field at fitness time.
Use the data the class have collected below, to work out how many laps of the track each student will need to walk on each of the 50 challenge days.
How do we get to school?
250, 186, 373, 1256, 812, 280
Week 3 Term 3
http://bestmaths.net/online/index.php/year-levels/year-7/year-7-topics/money/
Numbers in the news ...
Some numbers from Rio de Janerio in Brazil.
Venue of the 2016 Summer Olympic Games
Population of Rio: 6.4 million
Area of Rio: 1256 square kilometres (km2)
Founded: 1565
No. of days of competition: 17
No. of athletes competing: 10, 500
Medal events: 306
No. of security forces: 85, 000
The Steepest Street in the World
Dunedin, in New Zealand, claims to have the world's steepest paved road. However some people challenge Baldwin Street's slope and say mapping error has given it a gradient of 1 in 2.66, or 38%. However, it is almost impossible to ride a bike up or down it. Many of the stiffest road climbs for cyclists are on the Austrian side of the Dolomites (Halltall rises to 1482m in 7km at an average of 14%, its steepest stretch being 32%).
In France from the top of the legendary 1909m Mont Ventoux, there's around 1500m of descent in 21km averaging 7.5%; Iseran's 2770m peak offers 37km of descent and Alpe d'Huez has 21 hairpins.
San Francisco in the USA has some seriousoly steep streets. Take Lombard Street, a short streetcar ride from Fisherman's Wharf. This tourist photostop appeared for years in the Guinness Book of Records under its 'steepest street' entry, despite not even being the steepest street in San Francisco. At 1 in 5.5, or 18%, it's a mere slope compared to neighbouring Filbert St, San Francisco's actual steepest at 1 in 3.2, or 31.5% (22nd St is also 31.5%).
So it looks like Baldwin Street (pictured) may be the steepest after all.
Sample instructions to read to students
Sample picture
Write a summary about being introduced to Sumdog
What experience do you have in using computers for learning? What is liked about Sumdog? Do you enjoy learning maths? Has your attitude changed? Do you use Sumdog outside the classroom? If so are there any issues? What could be improved?
http://www.teachinabox.com.au/iteminfo.aspx?itemid=3058#productInfo
Doubling Strategy
Number theory
==
What is Problem Challenge?
Problem Challenge is a mathematics problem solving competition aimed primarily at children in years 7 and 8 but may be of interest to mathematically gifted children in year 6. It has been offered to schools throughout New Zealand for the past 25 years.Problem solving
https://www.maths.otago.ac.nz/pc/PCexamplesets.php
2015
SET THREE
Time allowed - 30 minutes
What is the smallest three-digit number whose digits add to 13?
If he coloured region 1 blue and region 2 red, what colour did he use for region X?
Give the last row from left to right, using * for the empty square (e.g. A*BC).
2015
SET FOUR
Time allowed - 30 minutes
In how many different ways can he do this?
How old is the teenager?
What is the value of ♥ ?
What is the number on the last numbered page?
NZ National Maths Contest - 10 Jun to 16 Jun
This contest has now finished. Congratulations to all those who took part!131Classes entered97Classes qualified2,288Students played824,920Questions answered694,670Correct answers
See the full entry list.
We didn't get in the top 50 this time round ... but we gave it a good go!!
Week 3 Term 2
Welcome to the contest!
Week 2 Term 2
==
Week 1 Term 2
Division and Subtraction to 1000 and also decimals
=
=
Week 11 Term 1
Take a look in the library ... there are lots of new books about maths!
http://nzmaths.co.nz/picture-books-mathematical-content
Task Instruction
Leo the Rabbit is climbing up a flight of 10 steps. Leo can only hop up 1 or 2 steps each time he hops. He never hops down, only up. How many different ways can Leo hop up the flight of 10 steps? Provide evidence to justify your thinking.=
=
If there is only one stair, then there is only one way to climb this stair.If there are three stairs, then the rabbit can take 3 small steps take a big step and then a small one or a small step followed by a big step.
If there are four stairs, then the rabbit can climb the stairs in
four small steps
two small steps and a large step
one small step, then a large, then a small
one large step, then two small steps
or two large steps
Thus we have
From what we did before there are 3 ways to get to step three and 2 ways to get to step two. Thus, there are 3 + 2 = 5 ways to get to step four.
Similarly for a 5 step flight of stairs there are 5 ways to get to step four and 3 ways to get to step three and thus there are 5 + 3 = 8 ways to get to step five.
So now we have
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10,944,...
Hence there are 89 nine ways for the rabbit to climb ten stairs (and 10,944 ways for it to climb 20 stairs!)
Level 4 number
Anno’s mysterious multiplying jar, by Masaichiro and Mitsumasa Anno
Publisher: Penguin Putman ISBN: 0698117530Activity based on this book.
The number devil: A mathematical adventure, by Hans Magnus Enzensberger
Publisher: Granta Books ISBN: 9781862078284Activity based on this book.
Maths curse, by Jon Scieszka and Lane Smith
Publisher: Viking Juvenile ISBN: 9780670861941Activity based on this book.
Fibonacci’s cows, by Ray Galvin
Activity based on this book.
Big numbers, by Mary and John Gribbin
Publisher: Wizard Books ISBN: 1840464313Activity based on this book.
A story of natural numbers, by David Demant
Publisher: Black Dog Books ISBN: 9781742030289Murderous maths numbers: the key to the universe, by Kjartan Poskitt
Publisher: Scholastic ISBN: 043998116650 Amazing Things Kids Need to Know about Mathematics, by Anne Rooney
Publisher: Quercus Books UK (2011) ISBN: 9780857386021Week 10 Term 1
http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/timetables/index.htm
http://www.ictgames.com/weight.html
http://www.tvokids.com/videos/2dand3dshapeswhyaretheydifferent
Welcome to the contest!
As it progresses, you'll find the latest scores on the leaderboards:
Contest leaderboards
Here are the results from the classes in your school:
Friday 11th March
Top 10 classes
Overall class scores are the average number of correct answers out of the students in that class. At least 10 students from the class must have played in order to get an average score.